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Business - Annual Profit Function

by Ruby
(Alto)










































Scenario:Annual profit in thousands of dollars is given by the function, P(x) = 12x - 100, where x is the number of items sold in thousands, x ≥ 10.

1.describe the meaning of the number 12 in the formula, in terms of its meaning in relation to the profit.
2.describe the meaning of the number -100 in the formula, in terms of its meaning in relation to the profit.
3.find the profit for 5 different values of x
4.graph the profit function over its given domain; use the 5 values calculated in part 3 to construct the graph and connect these points with a straight line in Excel or another graphing utility. Insert the graph in a Word file and attach the graph in a Word file to the class DB thread.
5.will this profit function have a maximum, if so, what is it?
6.what steps should the company take to prepare for your answer to part 5?

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May 18, 2012
Annual Profit Function
by: Staff


Part I

Question:

by Ruby
(Alto)


Scenario: Annual profit in thousands of dollars is given by the function, P(x) = 12x - 100, where x is the number of items sold in thousands, x ≥ 10.

1.describe the meaning of the number 12 in the formula, in terms of its meaning in relation to the profit.
2.describe the meaning of the number -100 in the formula, in terms of its meaning in relation to the profit.
3.find the profit for 5 different values of x
4.graph the profit function over its given domain; use the 5 values calculated in part 3 to construct the graph and connect these points with a straight line in Excel or another graphing utility. Insert the graph in a Word file and attach the graph in a Word file to the class DB thread.
5.will this profit function have a maximum, if so, what is it?
6.what steps should the company take to prepare for your answer to part 5?


Answer:


Scenario: Annual profit in thousands of dollars is given by the function, P(x) = 12x - 100, where x is the number of items sold in thousands, x ≥ 10.

1.describe the meaning of the number 12 in the formula, in terms of its meaning in relation to the profit.


The “12” is the gross revenue for each 1000 units sold



2.describe the meaning of the number -100 in the formula, in terms of its meaning in relation to the profit.

The -100 is the annual fixed expense for the company. It remains the same regardless of the number of units sold.



3.find the profit for 5 different values of x

x            P

15           80
20           140
25           200
30           260
35           320


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May 18, 2012
Annual Profit Function
by: Staff


---------------------------------------------
Part II


4.graph the profit function over its given domain; use the 5 values calculated in part 3 to construct the graph and connect these points with a straight line in Excel or another graphing utility. Insert the graph in a Word file and attach the graph in a Word file to the class DB thread.



Open the following link to view a graph of the profit function using the 5 values calculated above:


(1) If your browser is Firefox, click the following link to VIEW the graph; or if your browser is Chrome, Internet Explorer, Opera, or Safari (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page

http://www.solving-math-problems.com/images/graph-profit-function-excel-2012-05-17.png


(If you have trouble formatting the “x” axis using excel, add a comment to this post to let me know. I will add the instructions to this answer.)



5.will this profit function have a maximum, if so, what is it?

Mathematically the profit function has no maximum. The more units sold, the higher the profit.

In the real world the profit function will not be a straight line. There will have a maximum value.


6.what steps should the company take to prepare for your answer to part 5?


The profit function given is theoretical.

A company should carefully document the “x” and “p” values for the units it actually sells, and then plot a more realistic curve.


Thanks for writing.

Staff
www.solving-math-problems.com




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